% Mizar problem: t9_qc_trans,qc_trans,302,5 
fof(t9_qc_trans, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_qc_trans(D, A) & m1_qc_lang1(D))  =>  (! [E] :  (m1_valuat_1(E, D, C) =>  (! [F] :  (m1_valuat_1(F, A, C) =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(D), C, k2_valuat_1(D, C)) =>  (! [H] :  (m2_funct_2(H, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  ( (F=k5_relset_1(k6_qc_lang1(D), k2_margrel1(C), E, k6_qc_lang1(A)) & H=k5_relset_1(k3_qc_lang1(D), C, G, k3_qc_lang1(A)))  =>  (r1_valuat_1(D, C, k1_qc_trans(A, D, B), E, G) <=> r1_valuat_1(A, C, B, F, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_card_3, axiom,  (! [A] :  ( ~ (v4_card_3(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_card_3, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v1_relat_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_card_3, axiom,  (! [A, B] :  (v1_setfam_1(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v2_relat_1(C) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => v1_xboolean(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_margrel1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))) =>  ( (v1_funct_1(B) & v1_funct_2(B, A, k5_margrel1))  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & v1_margrel1(B)) ) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(A)) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) )  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, k9_funct_2(A, C)))) =>  ( (v1_funct_1(D) & v1_funct_2(D, B, k9_funct_2(A, C)))  =>  (v1_funct_1(D) &  (v1_funct_2(D, B, k9_funct_2(A, C)) & v1_funcop_1(D)) ) ) ) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_card_3, axiom,  (! [A] :  (v4_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_card_3(B)) ) ) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_card_3, axiom,  (! [A] :  (v2_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_card_3(B)) ) ) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d12_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k6_qc_lang1(A)) =>  (! [C] :  (m2_finseq_1(C, k2_qc_lang1(A)) =>  (k7_qc_lang1(A, B)=k3_finseq_1(C) => k10_qc_lang1(A, B, C)=k7_finseq_1(k12_finseq_1(k6_qc_lang1(A), B), C)) ) ) ) ) ) ) ).
fof(d13_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) => k11_qc_lang1(A, B)=B) ) ) ) ).
fof(d14_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k12_qc_lang1(A)=k9_finseq_1(k4_tarski(k5_numbers, k5_numbers))) ) ).
fof(d15_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) => k13_qc_lang1(A, B)=k7_finseq_1(k9_finseq_1(k4_tarski(1, k5_numbers)), k11_qc_lang1(A, B))) ) ) ) ).
fof(d16_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) => k14_qc_lang1(A, B, C)=k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(2, k5_numbers)), k11_qc_lang1(A, B)), k11_qc_lang1(A, C))) ) ) ) ) ) ).
fof(d17_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) => k15_qc_lang1(A, B, C)=k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(3, k5_numbers)), k12_finseq_1(k3_qc_lang1(A), B)), k11_qc_lang1(A, C))) ) ) ) ) ) ).
fof(d1_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k1_funct_4(A, B) <=>  (k9_xtuple_0(C)=k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B)) &  (! [D] :  (r2_hidden(D, k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B))) =>  ( (r2_hidden(D, k9_xtuple_0(B)) => k1_funct_1(C, D)=k1_funct_1(B, D))  &  ( ~ (r2_hidden(D, k9_xtuple_0(B)))  => k1_funct_1(C, D)=k1_funct_1(A, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] : k1_valuat_1(A, B)=k1_funct_2(k3_qc_lang1(A), B)) ) ) ).
fof(d29_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_qc_lang1(A)) => k23_qc_lang1(A, B)=a_2_1_qc_lang1(A, B)) ) ) ) ).
fof(d2_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k1_funct_2(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  &  (D=E &  (k9_xtuple_0(E)=A & r1_tarski(k10_xtuple_0(E), B)) ) ) ) ) ) ) ) ) ) ).
fof(d2_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k1_qc_lang1(A)=k10_xtuple_0(A)) ) ).
fof(d3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k2_qc_lang1(A)=k2_xboole_0(k2_zfmisc_1(k1_tarski(6), k4_ordinal1), k2_zfmisc_1(k2_tarski(4, 5), k1_qc_lang1(A)))) ) ).
fof(d3_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) => k1_qc_trans(A, B, C)=C) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k3_qc_lang1(A)=k2_zfmisc_1(k1_tarski(4), k1_qc_lang1(A))) ) ).
fof(d4_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) => k2_qc_trans(A, B, C)=C) ) ) ) ) ) ).
fof(d4_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(A))) )  =>  (! [E] :  (m1_subset_1(E, k2_margrel1(B)) =>  (! [F] :  (m2_funct_2(F, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (F=k5_valuat_1(A, B, C, D, E) <=>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (r2_tarski(k4_valuat_1(A, B, C, D, G), E) => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k7_margrel1)  &  ( (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k7_margrel1 => r2_tarski(k4_valuat_1(A, B, C, D, G), E))  &  ( ( ~ (r2_tarski(k4_valuat_1(A, B, C, D, G), E))  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k6_margrel1)  &  ~ ( (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k6_margrel1 & r2_tarski(k4_valuat_1(A, B, C, D, G), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d7_card_1, axiom,  (! [A] :  (! [B] :  (v3_card_1(B, A) <=> k1_card_1(B)=A) ) ) ).
fof(d7_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k6_qc_lang1(A)=a_1_0_qc_lang1(A)) ) ).
fof(d7_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m1_valuat_1(D, A, B) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, C, D, E) <=> k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, C), E)=k7_margrel1) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_funcop_1, axiom,  (! [A] :  (! [B] : k17_funcop_1(A, B)=k7_funcop_1(k1_tarski(A), B)) ) ).
fof(d9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) => k8_qc_lang1(A, B)=a_2_0_qc_lang1(A, B)) ) ) ) ).
fof(dt_k10_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k6_qc_lang1(A)) & m1_finseq_1(C, k2_qc_lang1(A))) )  => m1_subset_1(k10_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k11_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k11_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m2_finseq_1(k11_qc_lang1(A, B), k2_zfmisc_1(k4_ordinal1, k1_qc_lang1(A)))) ) ).
fof(dt_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m2_finseq_1(k12_finseq_1(A, B), A)) ) ).
fof(dt_k12_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A), k9_qc_lang1(A))) ) ).
fof(dt_k13_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k13_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k14_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k9_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k14_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k15_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k15_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k17_funcop_1, axiom, $true).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_finseq_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ).
fof(dt_k1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(dt_k1_qc_trans, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k1_qc_trans(A, B, C), k9_qc_lang1(B), k3_cqc_lang(B))) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_valuat_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xboolean, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k23_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_finseq_1(B, k2_qc_lang1(A)))  => m1_subset_1(k23_qc_lang1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_margrel1, axiom, $true).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_qc_trans, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  & m1_subset_1(C, k3_qc_lang1(A))) )  => m2_subset_1(k2_qc_trans(A, B, C), k2_qc_lang1(B), k3_qc_lang1(B))) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  => m1_funct_2(k2_valuat_1(A, B), k3_qc_lang1(A), B)) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xboolean, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_cqc_lang, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (m1_qc_lang1(B) &  (m1_subset_1(C, k8_qc_lang1(B, A)) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, A) & m1_finseq_1(D, k2_qc_lang1(B))) ) ) ) )  => m2_subset_1(k4_cqc_lang(A, B, C, D), k9_qc_lang1(B), k3_cqc_lang(B))) ) ).
fof(dt_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => m1_subset_1(k4_relset_1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m1_finseq_1(D, k2_qc_lang1(A))) )  & m1_subset_1(E, k2_valuat_1(A, B))) ) ) )  => m2_finseq_1(k4_valuat_1(A, B, C, D, E), B)) ) ).
fof(dt_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m2_subset_1(k5_cqc_lang(A), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_margrel1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k5_relset_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ).
fof(dt_k5_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m1_finseq_1(D, k2_qc_lang1(A))) )  & m1_subset_1(E, k2_margrel1(B))) ) ) )  => m2_funct_2(k5_valuat_1(A, B, C, D, E), k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) ).
fof(dt_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => m2_subset_1(k6_cqc_lang(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_margrel1, axiom, m1_subset_1(k6_margrel1, k5_margrel1)).
fof(dt_k6_qc_lang1, axiom, $true).
fof(dt_k7_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k7_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k7_margrel1, axiom, m1_subset_1(k7_margrel1, k5_margrel1)).
fof(dt_k7_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k6_qc_lang1(A)))  => v7_ordinal1(k7_qc_lang1(A, B))) ) ).
fof(dt_k7_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  (m1_valuat_1(D, A, B) & m1_subset_1(E, k8_qc_lang1(A, C))) ) ) )  => m1_subset_1(k7_valuat_1(A, B, C, D, E), k2_margrel1(B))) ) ).
fof(dt_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  =>  (v1_funct_1(k8_funcop_1(A, B, C)) &  (v1_funct_2(k8_funcop_1(A, B, C), B, A) & m1_subset_1(k8_funcop_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(B, A)))) ) ) ) ).
fof(dt_k8_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  => m1_subset_1(k8_qc_lang1(A, B), k1_zfmisc_1(k6_qc_lang1(A)))) ) ).
fof(dt_k8_valuat_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_valuat_1(C, A, B) & m1_subset_1(D, k3_cqc_lang(A))) ) )  => m2_funct_2(k8_valuat_1(A, B, C, D), k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) ).
fof(dt_k9_finseq_1, axiom,  (! [A] :  (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A))) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, k6_qc_lang1(A), k2_margrel1(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_qc_lang1(A), k2_margrel1(B))))) ) ) ) ) ) ).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(existence_m1_qc_lang1, axiom,  (? [A] : m1_qc_lang1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  =>  (? [C] : m1_valuat_1(C, A, B)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_card_3, axiom, v5_card_3(k4_ordinal1)).
fof(fc10_finset_1, axiom,  (! [A, B] :  (v1_finset_1(B) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc10_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_1(A, B))) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k17_funcop_1(A, B)) & v1_funct_1(k17_funcop_1(A, B))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_card_3, axiom,  (! [A, B] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k2_funcop_1(A, B))) ) ) ).
fof(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_1(A, B))) ) ) ).
fof(fc13_funcop_1, axiom,  (! [A, B] : v2_funct_1(k17_funcop_1(A, B))) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_finseq_1(k1_finseq_1(A))) ) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(A, B))) ) ).
fof(fc15_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => v4_funct_1(k2_tarski(A, B))) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc16_funcop_1, axiom,  (! [A, B] : v3_funct_1(k2_funcop_1(A, B))) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc18_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc18_funcop_1, axiom,  (! [A, B] : v4_relat_1(k2_funcop_1(A, B), A)) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc19_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc19_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(A))) ) ).
fof(fc19_funcop_1, axiom,  (! [A, B] : v4_relat_1(k17_funcop_1(A, B), k1_tarski(A))) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_card_3(k5_relat_1(A, B))) ) ) ).
fof(fc1_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc1_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
fof(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_1(A, B))) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_margrel1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_margrel1(A))) ) ) ).
fof(fc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc20_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_finset_1(k3_relat_1(B, A))) ) ) ).
fof(fc20_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k17_funcop_1(A, B))) ) ).
fof(fc21_finseq_1, axiom,  (! [A, B] :  (v3_finseq_1(A) => v3_finseq_1(k3_xboole_0(A, B))) ) ).
fof(fc21_finset_1, axiom,  (! [A, B] : v1_finset_1(k17_funcop_1(A, B))) ).
fof(fc21_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) &  (v4_relat_1(k2_funcop_1(A, B), A) &  (v1_funct_1(k2_funcop_1(A, B)) & v1_partfun1(k2_funcop_1(A, B), A)) ) ) ) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc22_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => v5_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc23_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k5_finseq_1(A))) ) ).
fof(fc23_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(C, B))  => v5_relat_1(k2_funcop_1(A, C), B)) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc24_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  ( ~ (v1_xboole_0(k7_finseq_1(A, B)))  & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc24_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) & v1_finset_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc24_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => v4_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc25_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, A)) &  (v1_funct_1(k7_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k7_finseq_1(B, A)))  & v1_finseq_1(k7_finseq_1(B, A))) ) ) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_finset_1(B))  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc27_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_card_3, axiom,  (! [A, B] :  (v1_card_1(B) => v1_card_3(k2_funcop_1(A, B))) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ~ (v1_xboole_0(k1_finseq_1(A))) ) ) ).
fof(fc2_finset_1, axiom,  (! [A, B] : v1_finset_1(k2_tarski(A, B))) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, A))) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_margrel1, axiom,  ~ (v1_xboole_0(k5_margrel1)) ).
fof(fc2_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k2_qc_lang1(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_tarski(A))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc32_finseq_1, axiom,  (! [A] : v3_card_1(k5_finseq_1(A), 1)) ).
fof(fc32_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v5_finset_1(k2_tarski(A, B))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc38_finseq_1, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v3_card_1(C, A) & v1_finseq_1(C)) ) )  &  (v1_relat_1(D) &  (v1_funct_1(D) &  (v3_card_1(D, B) & v1_finseq_1(D)) ) ) ) ) )  =>  (v1_relat_1(k7_finseq_1(C, D)) &  (v1_funct_1(k7_finseq_1(C, D)) &  (v3_card_1(k7_finseq_1(C, D), k2_xcmplx_0(A, B)) & v1_finseq_1(k7_finseq_1(C, D))) ) ) ) ) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_card_3, axiom,  (! [A, B] :  (v1_card_1(B) => v1_card_3(k17_funcop_1(A, B))) ) ).
fof(fc3_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(k1_finseq_1(A))) ) ).
fof(fc3_funcop_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B, A))) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_card_1(k1_finseq_1(A), A)) ) ).
fof(fc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k2_funcop_1(B, A))) ) ) ).
fof(fc4_margrel1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  => v1_xboolean(k1_funct_1(A, B))) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc54_finseq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, C)) &  (v5_relat_1(k7_finseq_1(B, C), A) &  (v1_funct_1(k7_finseq_1(B, C)) & v1_finseq_1(k7_finseq_1(B, C))) ) ) ) ) ).
fof(fc55_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v6_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v6_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc58_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v3_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc59_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v1_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
fof(fc5_margrel1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_card_3(B))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_margrel1(k5_relat_1(A, B))) ) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc60_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v2_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc61_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v6_valued_0(k5_finseq_1(A))) ) ).
fof(fc64_finseq_1, axiom,  (! [A] :  (v1_xreal_0(A) => v3_valued_0(k5_finseq_1(A))) ) ).
fof(fc65_finseq_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A))) ) ).
fof(fc66_finseq_1, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_valued_0(k5_finseq_1(A))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_finseq_1, axiom,  (! [A] :  (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k6_qc_lang1(A))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v2_card_3(k1_tarski(A))) ) ).
fof(fc7_finseq_1, axiom,  (! [A] : v1_finseq_1(k5_finseq_1(A))) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_margrel1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_margrel1(A))  => v2_card_3(k9_xtuple_0(A))) ) ).
fof(fc7_qc_lang1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_qc_lang1(B))  =>  ~ (v1_xboole_0(k8_qc_lang1(B, A))) ) ) ).
fof(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fraenkel_a_1_0_qc_lang1, axiom,  (! [A, B] :  (m1_qc_lang1(B) =>  (r2_hidden(A, a_1_0_qc_lang1(B)) <=>  (? [C, D] :  ( (v7_ordinal1(C) & m1_subset_1(D, k1_qc_lang1(B)))  &  (A=k4_tarski(C, D) & r1_xxreal_0(7, C)) ) ) ) ) ) ).
fof(fraenkel_a_2_0_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) & v7_ordinal1(C))  =>  (r2_hidden(A, a_2_0_qc_lang1(B, C)) <=>  (? [D] :  (m1_subset_1(D, k6_qc_lang1(B)) &  (A=D & k7_qc_lang1(B, D)=C) ) ) ) ) ) ).
fof(fraenkel_a_2_1_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) & m2_finseq_1(C, k2_qc_lang1(B)))  =>  (r2_hidden(A, a_2_1_qc_lang1(B, C)) <=>  (? [D] :  (v7_ordinal1(D) &  (A=k1_funct_1(C, D) &  (r1_xxreal_0(1, D) &  (r1_xxreal_0(D, k3_finseq_1(C)) & r2_tarski(k1_funct_1(C, D), k3_qc_lang1(B))) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_qc_trans, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  (v7_ordinal1(C) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(B))) ) ) )  =>  (r2_hidden(A, a_3_0_qc_trans(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_funct_1(D, E) &  (r1_xxreal_0(1, E) &  (r1_xxreal_0(E, k3_finseq_1(D)) & r2_tarski(k1_funct_1(D, E), k3_qc_lang1(B))) ) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_qc_trans, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_qc_trans(C, B) & m1_qc_lang1(C))  &  (v7_ordinal1(D) &  (v5_relat_1(E, k3_qc_lang1(B)) &  (v3_card_1(E, D) & m2_finseq_1(E, k2_qc_lang1(B))) ) ) ) )  =>  (r2_hidden(A, a_4_0_qc_trans(B, C, D, E)) <=>  (? [F] :  (v7_ordinal1(F) &  (A=k1_funct_1(E, F) &  (r1_xxreal_0(1, F) &  (r1_xxreal_0(F, k3_finseq_1(E)) & r2_tarski(k1_funct_1(E, F), k3_qc_lang1(C))) ) ) ) ) ) ) ) ).
fof(idempotence_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(A, A)=A) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc15_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  =>  (? [C] :  (m1_finseq_1(C, k2_qc_lang1(A)) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k2_qc_lang1(A)) &  (v5_relat_1(C, k3_qc_lang1(A)) &  (v1_funct_1(C) &  (v3_card_1(C, B) & v1_finseq_1(C)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_goedelcp, axiom,  (? [A] :  (m1_qc_lang1(A) & v4_card_3(A)) ) ).
fof(rc1_margrel1, axiom,  (? [A] :  (v4_finseq_1(A) & v2_card_3(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_qc_lang1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_qc_lang1(B))  =>  (? [C] :  (m1_finseq_1(C, k2_qc_lang1(B)) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k2_qc_lang1(B)) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v3_card_1(C, A) &  (v1_finseq_1(C) & v2_finseq_1(C)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_qc_lang1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) & v1_qc_trans(B, A)) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_margrel1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_qc_trans, axiom,  (! [A, B] :  ( ( (v4_card_3(A) & m1_qc_lang1(A))  &  (v4_card_3(B) & m1_qc_lang1(B)) )  =>  (? [C] :  (m1_qc_lang1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_card_3(C) &  (v1_qc_trans(C, A) & v1_qc_trans(C, B)) ) ) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_margrel1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v2_margrel1(A)) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_card_3, axiom,  (? [A] : v5_card_3(A)) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_finseq_1, axiom,  (! [A] : k1_funct_1(k9_finseq_1(A), 1)=A) ).
fof(rd1_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k1_funct_1(k2_funcop_1(A, B), C)=B) ) ).
fof(rd2_funcop_1, axiom,  (! [A, B] : k9_xtuple_0(k2_funcop_1(A, B))=A) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k11_cqc_lang(A, B, C)=k15_qc_lang1(A, B, C)) ) ).
fof(redefinition_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k12_finseq_1(A, B)=k5_finseq_1(B)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k2_finseq_1(A)=k1_finseq_1(A)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k2_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  => k2_valuat_1(A, B)=k1_valuat_1(A, B)) ) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k4_cqc_lang, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (m1_qc_lang1(B) &  (m1_subset_1(C, k8_qc_lang1(B, A)) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, A) & m1_finseq_1(D, k2_qc_lang1(B))) ) ) ) )  => k4_cqc_lang(A, B, C, D)=k10_qc_lang1(B, C, D)) ) ).
fof(redefinition_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k4_finseq_1(A)=k9_xtuple_0(A)) ) ).
fof(redefinition_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => k4_relset_1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
fof(redefinition_k4_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m1_finseq_1(D, k2_qc_lang1(A))) )  & m1_subset_1(E, k2_valuat_1(A, B))) ) ) )  => k4_valuat_1(A, B, C, D, E)=k3_relat_1(D, E)) ) ).
fof(redefinition_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k5_relset_1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => k6_cqc_lang(A, B)=k13_qc_lang1(A, B)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k6_margrel1, axiom, k6_margrel1=k1_xboolean).
fof(redefinition_k7_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k7_cqc_lang(A, B, C)=k14_qc_lang1(A, B, C)) ) ).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_k7_margrel1, axiom, k7_margrel1=k2_xboolean).
fof(redefinition_k7_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  (m1_valuat_1(D, A, B) & m1_subset_1(E, k8_qc_lang1(A, C))) ) ) )  => k7_valuat_1(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k8_funcop_1(A, B, C)=k2_funcop_1(B, C)) ) ).
fof(redefinition_k9_finseq_1, axiom,  (! [A] : k9_finseq_1(A)=k5_finseq_1(A)) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(reflexivity_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
fof(reflexivity_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_relset_1(A, B, C, C)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom, r1_xxreal_0(1, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r4, axiom, r1_xxreal_0(1, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r5, axiom, r1_xxreal_0(1, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r6, axiom, r1_xxreal_0(1, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r7, axiom, r1_xxreal_0(1, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ (r1_xxreal_0(2, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom, r1_xxreal_0(2, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r4, axiom, r1_xxreal_0(2, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r5, axiom, r1_xxreal_0(2, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r6, axiom, r1_xxreal_0(2, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r7, axiom, r1_xxreal_0(2, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r1, axiom,  ~ (r1_xxreal_0(3, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r2, axiom,  ~ (r1_xxreal_0(3, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom, r1_xxreal_0(3, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r4, axiom, r1_xxreal_0(3, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r5, axiom, r1_xxreal_0(3, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r6, axiom, r1_xxreal_0(3, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r7, axiom, r1_xxreal_0(3, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r1, axiom,  ~ (r1_xxreal_0(4, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r4_r2, axiom,  ~ (r1_xxreal_0(4, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r4_r3, axiom,  ~ (r1_xxreal_0(4, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r4_r4, axiom, r1_xxreal_0(4, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r5, axiom, r1_xxreal_0(4, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r6, axiom, r1_xxreal_0(4, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r7, axiom, r1_xxreal_0(4, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r1, axiom,  ~ (r1_xxreal_0(5, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r2, axiom,  ~ (r1_xxreal_0(5, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r3, axiom,  ~ (r1_xxreal_0(5, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r4, axiom,  ~ (r1_xxreal_0(5, 4)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r5, axiom, r1_xxreal_0(5, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r6, axiom, r1_xxreal_0(5, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r7, axiom, r1_xxreal_0(5, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r1, axiom,  ~ (r1_xxreal_0(6, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r2, axiom,  ~ (r1_xxreal_0(6, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r3, axiom,  ~ (r1_xxreal_0(6, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r4, axiom,  ~ (r1_xxreal_0(6, 4)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r5, axiom,  ~ (r1_xxreal_0(6, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r6, axiom, r1_xxreal_0(6, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r7, axiom, r1_xxreal_0(6, 7)).
fof(rqLessOrEqual__r1_xxreal_0__r7_r1, axiom,  ~ (r1_xxreal_0(7, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r2, axiom,  ~ (r1_xxreal_0(7, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r3, axiom,  ~ (r1_xxreal_0(7, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r4, axiom,  ~ (r1_xxreal_0(7, 4)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r5, axiom,  ~ (r1_xxreal_0(7, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r6, axiom,  ~ (r1_xxreal_0(7, 6)) ).
fof(rqLessOrEqual__r1_xxreal_0__r7_r7, axiom, r1_xxreal_0(7, 7)).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom, k2_xcmplx_0(1, 2)=3).
fof(rqRealAdd__k2_xcmplx_0__r1_r3_r4, axiom, k2_xcmplx_0(1, 3)=4).
fof(rqRealAdd__k2_xcmplx_0__r1_r4_r5, axiom, k2_xcmplx_0(1, 4)=5).
fof(rqRealAdd__k2_xcmplx_0__r1_r5_r6, axiom, k2_xcmplx_0(1, 5)=6).
fof(rqRealAdd__k2_xcmplx_0__r1_r6_r7, axiom, k2_xcmplx_0(1, 6)=7).
fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom, k2_xcmplx_0(2, 1)=3).
fof(rqRealAdd__k2_xcmplx_0__r2_r2_r4, axiom, k2_xcmplx_0(2, 2)=4).
fof(rqRealAdd__k2_xcmplx_0__r2_r3_r5, axiom, k2_xcmplx_0(2, 3)=5).
fof(rqRealAdd__k2_xcmplx_0__r2_r4_r6, axiom, k2_xcmplx_0(2, 4)=6).
fof(rqRealAdd__k2_xcmplx_0__r2_r5_r7, axiom, k2_xcmplx_0(2, 5)=7).
fof(rqRealAdd__k2_xcmplx_0__r3_r1_r4, axiom, k2_xcmplx_0(3, 1)=4).
fof(rqRealAdd__k2_xcmplx_0__r3_r2_r5, axiom, k2_xcmplx_0(3, 2)=5).
fof(rqRealAdd__k2_xcmplx_0__r3_r3_r6, axiom, k2_xcmplx_0(3, 3)=6).
fof(rqRealAdd__k2_xcmplx_0__r3_r4_r7, axiom, k2_xcmplx_0(3, 4)=7).
fof(rqRealAdd__k2_xcmplx_0__r4_r1_r5, axiom, k2_xcmplx_0(4, 1)=5).
fof(rqRealAdd__k2_xcmplx_0__r4_r2_r6, axiom, k2_xcmplx_0(4, 2)=6).
fof(rqRealAdd__k2_xcmplx_0__r4_r3_r7, axiom, k2_xcmplx_0(4, 3)=7).
fof(rqRealAdd__k2_xcmplx_0__r5_r1_r6, axiom, k2_xcmplx_0(5, 1)=6).
fof(rqRealAdd__k2_xcmplx_0__r5_r2_r7, axiom, k2_xcmplx_0(5, 2)=7).
fof(rqRealAdd__k2_xcmplx_0__r6_r1_r7, axiom, k2_xcmplx_0(6, 1)=7).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_r3_r3, axiom, k3_xcmplx_0(1, 3)=3).
fof(rqRealMult__k3_xcmplx_0__r1_r4_r4, axiom, k3_xcmplx_0(1, 4)=4).
fof(rqRealMult__k3_xcmplx_0__r1_r5_r5, axiom, k3_xcmplx_0(1, 5)=5).
fof(rqRealMult__k3_xcmplx_0__r1_r6_r6, axiom, k3_xcmplx_0(1, 6)=6).
fof(rqRealMult__k3_xcmplx_0__r1_r7_r7, axiom, k3_xcmplx_0(1, 7)=7).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_r2_r4, axiom, k3_xcmplx_0(2, 2)=4).
fof(rqRealMult__k3_xcmplx_0__r2_r3_r6, axiom, k3_xcmplx_0(2, 3)=6).
fof(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, k3_xcmplx_0(3, 1)=3).
fof(rqRealMult__k3_xcmplx_0__r3_r2_r6, axiom, k3_xcmplx_0(3, 2)=6).
fof(rqRealMult__k3_xcmplx_0__r4_r1_r4, axiom, k3_xcmplx_0(4, 1)=4).
fof(rqRealMult__k3_xcmplx_0__r5_r1_r5, axiom, k3_xcmplx_0(5, 1)=5).
fof(rqRealMult__k3_xcmplx_0__r6_r1_r6, axiom, k3_xcmplx_0(6, 1)=6).
fof(rqRealMult__k3_xcmplx_0__r7_r1_r7, axiom, k3_xcmplx_0(7, 1)=7).
fof(s1_cqc_lang__e7_19__qc_trans, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v1_qc_trans(C, A) & m1_qc_lang1(C)) ) )  =>  ( (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [F] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [G] :  (v7_ordinal1(G) =>  (! [H] :  ( (v5_relat_1(H, k3_qc_lang1(A)) &  (v3_card_1(H, G) & m2_finseq_1(H, k2_qc_lang1(A))) )  =>  (! [I] :  (m2_subset_1(I, k6_qc_lang1(A), k8_qc_lang1(A, G)) =>  ( (! [J] :  (m1_valuat_1(J, C, B) =>  (! [K] :  (m1_valuat_1(K, A, B) =>  (! [L] :  (m2_funct_2(L, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [M] :  (m2_funct_2(M, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (K=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), J, k6_qc_lang1(A)) & M=k5_relset_1(k3_qc_lang1(C), B, L, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, k5_cqc_lang(A)), J, L) <=> r1_valuat_1(A, B, k5_cqc_lang(A), K, M)) ) ) ) ) ) ) ) ) )  &  ( (! [N] :  (m1_valuat_1(N, C, B) =>  (! [O] :  (m1_valuat_1(O, A, B) =>  (! [P] :  (m2_funct_2(P, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [Q] :  (m2_funct_2(Q, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (O=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), N, k6_qc_lang1(A)) & Q=k5_relset_1(k3_qc_lang1(C), B, P, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, k4_cqc_lang(G, A, I, H)), N, P) <=> r1_valuat_1(A, B, k4_cqc_lang(G, A, I, H), O, Q)) ) ) ) ) ) ) ) ) )  &  ( ( (! [R] :  (m1_valuat_1(R, C, B) =>  (! [S] :  (m1_valuat_1(S, A, B) =>  (! [T] :  (m2_funct_2(T, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [U] :  (m2_funct_2(U, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (S=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), R, k6_qc_lang1(A)) & U=k5_relset_1(k3_qc_lang1(C), B, T, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, D), R, T) <=> r1_valuat_1(A, B, D, S, U)) ) ) ) ) ) ) ) ) )  =>  (! [V] :  (m1_valuat_1(V, C, B) =>  (! [W] :  (m1_valuat_1(W, A, B) =>  (! [X] :  (m2_funct_2(X, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [Y] :  (m2_funct_2(Y, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (W=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), V, k6_qc_lang1(A)) & Y=k5_relset_1(k3_qc_lang1(C), B, X, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, k6_cqc_lang(A, D)), V, X) <=> r1_valuat_1(A, B, k6_cqc_lang(A, D), W, Y)) ) ) ) ) ) ) ) ) ) )  &  ( ( ( (! [Z] :  (m1_valuat_1(Z, C, B) =>  (! [A1] :  (m1_valuat_1(A1, A, B) =>  (! [B1] :  (m2_funct_2(B1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [C1] :  (m2_funct_2(C1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (A1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), Z, k6_qc_lang1(A)) & C1=k5_relset_1(k3_qc_lang1(C), B, B1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, D), Z, B1) <=> r1_valuat_1(A, B, D, A1, C1)) ) ) ) ) ) ) ) ) )  &  (! [D1] :  (m1_valuat_1(D1, C, B) =>  (! [E1] :  (m1_valuat_1(E1, A, B) =>  (! [F1] :  (m2_funct_2(F1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [G1] :  (m2_funct_2(G1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (E1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), D1, k6_qc_lang1(A)) & G1=k5_relset_1(k3_qc_lang1(C), B, F1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, E), D1, F1) <=> r1_valuat_1(A, B, E, E1, G1)) ) ) ) ) ) ) ) ) ) )  =>  (! [H1] :  (m1_valuat_1(H1, C, B) =>  (! [I1] :  (m1_valuat_1(I1, A, B) =>  (! [J1] :  (m2_funct_2(J1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [K1] :  (m2_funct_2(K1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (I1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), H1, k6_qc_lang1(A)) & K1=k5_relset_1(k3_qc_lang1(C), B, J1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, k7_cqc_lang(A, D, E)), H1, J1) <=> r1_valuat_1(A, B, k7_cqc_lang(A, D, E), I1, K1)) ) ) ) ) ) ) ) ) ) )  &  ( (! [L1] :  (m1_valuat_1(L1, C, B) =>  (! [M1] :  (m1_valuat_1(M1, A, B) =>  (! [N1] :  (m2_funct_2(N1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [O1] :  (m2_funct_2(O1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (M1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), L1, k6_qc_lang1(A)) & O1=k5_relset_1(k3_qc_lang1(C), B, N1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, D), L1, N1) <=> r1_valuat_1(A, B, D, M1, O1)) ) ) ) ) ) ) ) ) )  =>  (! [P1] :  (m1_valuat_1(P1, C, B) =>  (! [Q1] :  (m1_valuat_1(Q1, A, B) =>  (! [R1] :  (m2_funct_2(R1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [S1] :  (m2_funct_2(S1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (Q1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), P1, k6_qc_lang1(A)) & S1=k5_relset_1(k3_qc_lang1(C), B, R1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, k11_cqc_lang(A, F, D)), P1, R1) <=> r1_valuat_1(A, B, k11_cqc_lang(A, F, D), Q1, S1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [T1] :  (m1_valuat_1(T1, C, B) =>  (! [U1] :  (m1_valuat_1(U1, A, B) =>  (! [V1] :  (m2_funct_2(V1, k3_qc_lang1(C), B, k2_valuat_1(C, B)) =>  (! [W1] :  (m2_funct_2(W1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (U1=k5_relset_1(k6_qc_lang1(C), k2_margrel1(B), T1, k6_qc_lang1(A)) & W1=k5_relset_1(k3_qc_lang1(C), B, V1, k3_qc_lang1(A)))  =>  (r1_valuat_1(C, B, k1_qc_trans(A, C, D), T1, V1) <=> r1_valuat_1(A, B, D, U1, W1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc5_boole, axiom,  ~ (v1_xboole_0(5)) ).
fof(spc5_numerals, axiom,  (v2_xxreal_0(5) & m1_subset_1(5, k4_ordinal1)) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc6_boole, axiom,  ~ (v1_xboole_0(6)) ).
fof(spc6_numerals, axiom,  (v2_xxreal_0(6) & m1_subset_1(6, k4_ordinal1)) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(spc7_boole, axiom,  ~ (v1_xboole_0(7)) ).
fof(spc7_numerals, axiom,  (v2_xxreal_0(7) & m1_subset_1(7, k4_ordinal1)) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(symmetry_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) => r2_relset_1(A, B, D, C)) ) ) ).
fof(t102_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (! [C] :  (r2_tarski(C, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, C), A)) ) ) ) ) ).
fof(t12_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k2_xboole_0(A, B)=B) ) ) ).
fof(t13_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) => k1_funct_1(k1_funct_4(A, B), C)=k1_funct_1(B, C)) ) ) ) ) ) ).
fof(t17_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => r1_tarski(k10_xtuple_0(k1_funct_4(A, B)), k2_xboole_0(k10_xtuple_0(A), k10_xtuple_0(B)))) ) ) ) ).
fof(t17_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_funct_2(C, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m1_valuat_1(E, A, B) =>  (r1_valuat_1(A, B, k6_cqc_lang(A, D), E, C) <=>  ~ (r1_valuat_1(A, B, D, E, C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_funct_2(C, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [F] :  (m1_valuat_1(F, A, B) =>  (r1_valuat_1(A, B, k7_cqc_lang(A, D, E), F, C) <=>  (r1_valuat_1(A, B, D, F, C) & r1_valuat_1(A, B, E, F, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (r2_hidden(A, k1_finseq_1(B)) <=>  (r1_xxreal_0(1, A) & r1_xxreal_0(A, B)) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  ( (v5_relat_1(C, k3_qc_lang1(A)) &  (v3_card_1(C, B) & m2_finseq_1(C, k2_qc_lang1(A))) )  =>  (! [D] :  (m2_subset_1(D, k6_qc_lang1(A), k8_qc_lang1(A, B)) => k7_qc_lang1(A, D)=k3_finseq_1(C)) ) ) ) ) ) ) ) ).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t28_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k3_xboole_0(A, B)=A) ) ) ).
fof(t29_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [F] :  (m1_valuat_1(F, A, B) =>  (r1_valuat_1(A, B, k11_cqc_lang(A, C, E), F, D) <=>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [H] :  (m2_subset_1(H, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=H)  => k3_funct_2(k3_qc_lang1(A), B, G, H)=k3_funct_2(k3_qc_lang1(A), B, D, H)) ) )  => r1_valuat_1(A, B, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t32_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_funct_2(C, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D] :  (m1_valuat_1(D, A, B) => r1_valuat_1(A, B, k5_cqc_lang(A), D, C)) ) ) ) ) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t46_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  ( (k9_xtuple_0(C)=k3_xboole_0(k9_xtuple_0(B), A) &  (! [D] :  (r2_hidden(D, k9_xtuple_0(C)) => k1_funct_1(C, D)=k1_funct_1(B, D)) ) )  => C=k5_relat_1(B, A)) ) ) ) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  => r1_tarski(k3_qc_lang1(A), k3_qc_lang1(B))) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t59_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [E] :  ( (v5_relat_1(E, k3_qc_lang1(A)) &  (v3_card_1(E, B) & m2_finseq_1(E, k2_qc_lang1(A))) )  => r2_relset_1(k4_ordinal1, C, k4_valuat_1(A, C, B, E, D), k4_relset_1(k4_ordinal1, k2_qc_lang1(A), k3_qc_lang1(A), C, E, k5_relset_1(k3_qc_lang1(A), C, D, k23_qc_lang1(A, E))))) ) ) ) ) ) ) ) ) ) ).
fof(t5_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(A))) )  =>  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(B))) ) ) ) ) ) ) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  (m2_subset_1(C, k6_qc_lang1(A), k8_qc_lang1(A, B)) =>  (! [D] :  ( (v1_qc_trans(D, A) & m1_qc_lang1(D))  => m2_subset_1(C, k6_qc_lang1(D), k8_qc_lang1(D, B))) ) ) ) ) ) ) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t6_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, B) & m2_finseq_1(D, k2_qc_lang1(A))) )  =>  (! [E] :  (m1_valuat_1(E, A, C) =>  (! [F] :  (m2_subset_1(F, k6_qc_lang1(A), k8_qc_lang1(A, B)) => r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, E, k4_cqc_lang(B, A, F, D)), k5_valuat_1(A, C, B, D, k7_valuat_1(A, C, B, E, F)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t71_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) => k5_relat_1(k5_relat_1(C, A), B)=k5_relat_1(C, k3_xboole_0(A, B))) ) ) ) ).
fof(t72_funcop_1, axiom,  (! [A] :  (! [B] : k1_funct_1(k17_funcop_1(A, B), A)=B) ) ).
fof(t74_funcop_1, axiom,  (! [A] :  (! [B] : r2_hidden(A, k9_xtuple_0(k17_funcop_1(A, B)))) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t83_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  (! [D] :  ( ~ (B=D)  => k1_funct_1(k1_funct_4(A, k17_funcop_1(B, C)), D)=k1_funct_1(A, D)) ) ) ) ) ) ).
fof(t89_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_card_1(B, A) & v1_finseq_1(B)) ) )  => k4_finseq_1(B)=k2_finseq_1(A)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_funcop_1, axiom,  (! [A] :  (! [B] :  ( ~ (A=k1_xboole_0)  => k10_xtuple_0(k2_funcop_1(A, B))=k1_tarski(B)) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
fof(t92_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_tarski(C, k1_funct_2(A, B)) =>  (k9_xtuple_0(C)=A & r1_tarski(k10_xtuple_0(C), B)) ) ) ) ) ) ).
